analysis of l bracket

8/10/2019 Analysis of L Bracket

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3: Static analysis of an L-bracket

Topics covered

?

Stress singularities

? Differences between modeling errors and discretization errors

? Using mesh controls

? Analysis in different SolidWorks configurations

? Nodal stresses, element stresses

Project description

An L-shaped bracket (the file L BRACKET) is supported and loaded asshown in Figure 3-1. We would like to find the displacements and stressescaused by a 1000N bending load. In particular, we are interested in stresses inthe corner where the 2mm fillet is located. Since the radius of the fillet issmall compared to the overall size of the model, we decide to suppress it. Aswe will soon prove, suppressing the fillet is a bad mistake!

Figure 3-1: Loads and supports applied to the L BRACKET model

The geometry of the L BRACKET includes a fillet, which will be mistakenlysuppressed, leaving in its place a sharp re-entrant corner.

TheL BRACKETmodel has two configurations: 01 sharp edgeand 02 roundedge. Change to the 01 sharp edgeconfiguration by double clicking theconfiguration name. The material (Alloy steel) is applied to the SolidWorksmodel and is automatically transferred to SolidWorks Simulation.

1000N load uniformly

distributed over the

end face

Fixed restraint to the

top face

Fillet


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Procedure

Make sure the model is in configuration 01 sharp edge. Following the samesteps as those described in chapter 2, define a study calledmesh 1and definea Fixed restraint to the top face shown in Figure 3-1. Define the load usingthe Force/Torque window choices shown in Figure 3-2.

Figure 3-2: Force definition window specifies force in a selected direction.The direction is specified as normal to the Top reference plane.

The Top reference plane is used as a reference to determine force direction.The reference plane can be conveniently selected from the fly out SolidWorksmenu to the right of the Force/Torque window.

Fly-out menu

Geometric entity

where load is applied

Geometric entity

used to define load

direction


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Next, make sure the mesh setting is Standard meshand mesh the model withsecond order tetrahedral elements, accepting the default element size. Thefinite element mesh is shown in Figure 3-3.

Figure 3-3: The finite element mesh created with default settings of the meshgenerator

To show the Mesh menu, right-click the mesh folder. In this mesh, the globalelement size is 4.76 mm.

The displacement and stress results obtained in the mesh 1study are shownin Figure 3-4.


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Figure 3-4: Displacements (top) and von Mises stresses results (bottom)produced using study mesh 1

The maximum displacement is 0.247 mm and the maximum von Mises stress is81 MPa. As explained later, these stress results are meaningless.


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Now we will investigate how using smaller elements affects the results. Inchapter 2, we did this by refining the mesh uniformly so that the entire modelwas meshed with elements of a smaller size. Here we will use a differenttechnique. Having noticed that the stress concentration is near the sharp re-entrant corner, we will refine the mesh locally in that area by applying meshcontrols. The element size everywhere else will remain the same as it was

before: 4.76mm.

Copy the mesh1study into a new study, naming it mesh2. Select the edgewhere mesh controls will be applied, then right-click theMeshfolder in themesh2study dialog (this folder is currently empty) to display the pop-upmenu shown in Figure 3-5.

Figure 3-5: Mesh pop-up menu

Select Apply Mesh Controlby right-clicking on the Mesh folder, whichopens the Mesh Controlwindow (Figure 3-6). It is also possible to open the

Mesh Controlwindow first and then select the desired entity or entities (herethe re-entrant edge) where mesh controls are being applied.

Mesh controls


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Figure 3-6: Mesh Control window

Mesh controls allow for the definition of a local element size on selectedentities. Accept the default values of the Mesh Control window.

The element size along the selected edge is now controlled independently ofthe global element size. Mesh control can also be applied to vertices, facesand to entire components of assemblies.Having defined the mesh control,

create a mesh with the same global element size as before (4.76 mm), whilemaking elements along the specified edge to be 2.38 mm. The added meshcontrols display as the Control-1icon in theMeshfolder and can be editedusing a pop-up menu displayed by right-clicking the mesh control icon(Figure 3-7).

Element size along the

selected entity

Relative element sizein adjacent layers of

elements


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Figure 3-7: Pop-up menu for the mesh control icon

The mesh with applied control (also called mesh bias) is shown in Figure 3-8.

Figure 3-8: Mesh with applied controls (mesh bias)

The mesh in study mesh2 is refined along the selected edge.

Mesh bias along this edge

If desired, select Edit

Definition to open the

Mesh Control window and

edit the mesh control

(mesh bias)


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The maximum displacements and stress results obtained in study mesh2are 2.47697 mm and 74.1 MPa respectively. The number of digits shownin a result plot is controlled using Chart Options (right-click on a plot andselect Chart Options).

Now repeat the same exercise three more times using progressively smallerelements along the sharp re-entrant edge. Create three studies with an elementsize along the sharp-re entrant edge as shown in Figure 3-9.

Figure 3-9: Mesh Control windows in studies mesh3, mesh4, and mesh5defining the element size along the sharp re-entrant edge.

Study mesh 3:

1.19mm

Study mesh 4:

0.60mm

Study mesh 4:

0.30mm


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The summary of results of all five studies is shown in Figures 3-10 and 3-11.

StudyElement size h

[mm]

Max. resultant

displacement

[mm]

Max. von

Mises stress

[MPa]

mesh 1 4.76 0.2473 81

mesh 2 2.38 0.2478 73

mesh 3 1.19 0.2481 112

mesh 4 0.60 0.2484 132

mesh 5 0.30 0.2485 188

Figure 3-10: Summary of maximum displacement results and maximum vonMises stress results

Figure 3-11: Max. resultant displacement (left) and max. von Mises stress(right) as a function of 1/h (h is the element size (Figure 2-15) along the sharpre-entrant edge

The local drop in stress magnitude for study mesh 2 is caused by shifting themaximum stress location between studies mesh1 and mesh2.

Max. resultant displacement Max. von Mises stress

MPamm

1/h 1/h


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Upon examining Figures 3-10 and 3-11, we notice that while each meshrefinement brings about an increase in the maximum displacement, thedifference between consecutive results decreases. The increase ofdisplacement results are so minute that the results need four decimal places toshow the difference. The first study, without any mesh refinement providesaccurate displacement results.

The stress behaves very differently. Each mesh refinement brings about anincrease in the maximum stress. The difference between consecutive resultsincreases, proving that the maximum stress result is divergent.

We could continue with this exercise of progressive mesh refinement either:

? Locally, near the sharp re-entrant, as we have done here by means ofmesh controls, or

? Globally, by reducing the global element size, as we did in chapter 2.

Given enough time and patience, we can produce results showing any stressmagnitude we want. All that is necessary is to make the element size smallenough! We should avoid a temptation to make any conclusions based on the

stress graph in Figure 3-11 because all these results are meaningless!

The reason for divergent stress results is not that the finite element modelis incorrect, but that the finite element model is based on the wrongmathematical model.

According to the theory of elasticity, stress in a sharp re-entrant corneris infinite. A mathematician would say that stress in a sharp re-entrant corneris singular. Stress results in a sharp re-entrant corner are completelydependent on mesh size: the smaller the element, the higher the stress.Therefore, we must repeat this exercise after un-suppressing the fillet, whichis done by changing from configuration 01 sharp edge to 02 round edge in theSolidWorks Configuration Manager.


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Notice that after we return from the Configuration Manager window to theSolidWorks Simulationwindow, all studies pertaining to the model inconfiguration 01 sharp cornerare not accessible. They can be accessed only ifthe model configuration is changed back to 01 sharp corner (Figure 3-12).

Figure 3-12: Studies become inaccessible when the model configuration ischanged to a configuration other than that corresponding to the now grayed-out studies.

The SolidWorks model can be changed to a configuration correspondingto a given study by right-clicking the study icon and selecting Activate SWconfiguration.


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To analyze the bracket with the fillet, define a study named round edge. CopytheFixturesandExternal Loadsfolders from any inactive studies to the roundedgestudy by clicking them and dragging them to the new study tab (Figure3-13).

.

Figure 3-13: CopyingFixturesandExternal Loadsfrom study mesh2tostudyround edge

Entities can be copied between studies by dragging them and dropping theminto a study tab as shown, even if the source information is from aninaccessible study.


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Meshing with the default element size and Standard Mesh properties produceselements with an excessive turn angle in the area where it is particularlyimportant to have a correct mesh (Figure 3-14).

Figure 3-14: A mesh created as a Standard Mesh with a default element size is

not acceptable because of the high turn angle

Here, the turn angle of the element meshing the fillet is 90. Just one elementcovers the 90 angle, as shown.

To eliminate excessive turn angles from areas where stresses are of particularinterest we use the Curvature based meshoption (Figure 3-15).

Standard

mesh

Element turn

angle 90


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Figure 3-15: Curvature based mesh assures correct meshing of curved faces

With the minimum number of elements in a circle (360) set to 12, an elementturn angle is no more than 360/12=30.

The element size growth ratio controls the transition between the refined meshon curved faces and the coarser mesh on flat faces.

It is generally recommended that the turn angle does not exceed 30 insensitive locations where stresses must be correctly modeled.

Curvature

based mesh

Minimum number

of elements in a

circle 12

Global element

size 5mm

Using the above settings,

a minimum of 3 elements

are created on a 90 fillet

Element size

growth ratio 1.6


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The L-BRACKET example is a good place to review the different waysof displaying stress results. Stresses can be presented either as Node Valuesor Element Values. To select either node values or element values, right-clickthe plot icon and select Edit Definition. This will open the Stress Plotwindow. Figure 3-16 shows the nodevalues of von Mises stress results

produced in the study round edge.

Figure 3-16: Von Mises stresses displayed as nodevalues

The irregularities in the shape of discrete fringes showing nodal stress results(left) may be used to decide if more mesh refinement is needed in the area of a

stress concentration. Here, regular shapes indicate sufficient meshrefinement.

The maximum stress (120MPa) is now bounded. In the convergence process itwill converge to a finite value, close to the one shown in Figure 3-16. Again,we must resist temptation to compare this result to the maximum stress results

produced by the studies using the sharp re-entrant edge because the results areall meaningless.

Node

values


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Figure 3-17 shows the elementvalues of von Mises stress results produced inthe study round edge.

Figure 3-17 Von Mises stresses displayed as element values

Element values are not averaged across different elements. A single stressvalue is assigned to each element.

Element

values


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As was explained in chapter 1, nodal displacements are computed first, fromwhich strains and then stresses are calculated. Stresses are first calculatedinside the element at certain locations, called Gauss points. Next, stress resultsare extrapolated to all of the elements nodes. If one node belongs to morethan one element (which is always the case unless it is a vertex node), then thestress results from all the elements sharing a given node are averaged and one

stress value, called a node value, is reported for each node.

An alternate procedure to present stress results is by obtaining stresses atGauss points, then averaging them in between themselves. This means thatone stress value is calculated for the element. This stress value is called anelement value.

Nodevalues are used more often because they offer smoothed out, continuousstress results. However, examination of elementvalues provides importantfeedback on the quality of the results. If elementvalues in two adjacentelements differ too much it indicates that the element size at this location istoo large to properly model the stress gradient. By examining the elementvalues, we can locate mesh deficiencies without running a convergence

analysis.

To decide how much is too much of a difference requires some experience.As a general guideline, we can say that if the element values of stress inadjacent elements are apart by several colors on the default color chart, thena more refined mesh should be used. You are encouraged to perform aconverge analysis using a Curvature Based mesh.


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analysis of l bracket

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